aeCharacteristic function

Asymptotic Expansion - Characteristic Function

aeCharacteristic(..., ae, eps = 1, order = NULL)

Arguments

• ...: named argument, data.frame, list, or environment specifying the grid to evaluate the characteristic function. See examples.
• ae: an object of class yuima.ae-class.
• eps: numeric. The intensity of the perturbation.
• order: integer. The expansion order. If NULL (default), it uses the maximum order used in ae.

Returns

Characteristic function evaluated on the given grid.

Examples

## Not run:

# model
gbm <- setModel(drift = 'mu*x', diffusion = 'sigma*x', solve.variable = 'x')

# settings
xinit <- 100
par <- list(mu = 0.01, sigma = 0.2)
sampling <- setSampling(Initial = 0, Terminal = 1, n = 1000)

# asymptotic expansion
approx <- ae(model = gbm, sampling = sampling, order = 4, true.parameter = par, xinit = xinit)

# The following are all equivalent methods to specify the grid via ....
# Notice that the character 'u1' corresponds to the 'u.var' of the ae object.
approx@u.var

# 1) named argument  
u1 <- seq(0, 1, by = 0.1)
psi <- aeCharacteristic(u1 = u1, ae = approx, order = 4)
# 2) data frame
df <- data.frame(u1 = seq(0, 1, by = 0.1))
psi <- aeCharacteristic(df, ae = approx, order = 4)
# 3) environment
env <- new.env()
env$u1 <- seq(0, 1, by = 0.1)
psi <- aeCharacteristic(env, ae = approx, order = 4)
# 4) list
lst <- list(u1 = seq(0, 1, by = 0.1))
psi <- aeCharacteristic(lst, ae = approx, order = 4)
## End(Not run)